Well, you can already do that through extended validation. I'm not sure requiring it would be desirable, and doing this would need a better reason than it being better than nothing.
The philosophy of HTML5 seems to be allowing applicants to do a lot of things which don't require much trust to be placed in them (and most applications don't need much), rather than security through asking the user's permission (e.g. most desktop OSs), when they are unlikely to have much idea which developers they should trust, or through accountability/review (e.g. iOS), which adds barriers to entry.
The philosophy of HTML5 seems to be allowing applicants to do a lot of things which don't require much trust to be placed in them (and most applications don't need much), rather than security through asking the user's permission (e.g. most desktop OSs), when they are unlikely to have much idea which developers they should trust, or through accountability/review (e.g. iOS), which adds barriers to entry.